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FaDIn: Fast Discretized Inference for Hawkes Processes with General Parametric Kernels
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Discretize the events onto a grid with stepsize Delta (coarse, e.g. 0.01) when fitting FaDIn with a finite-support kernel (ablation) | FaDIn · Synthetic 1-dim Truncated Gaussian kernel, varying T and Delta | l2 error of parameter estimates | No clear effect |
| Use the discretized l2 loss with precomputations instead of the negative log-likelihood (ablation) | FaDIn · Univariate simulated Hawkes, RC/TG/TE kernels, Delta=0.01, T=10^5 | computational time: ~1000x faster at T=10^5; ~5x at T=10^2 | Helped |
| Use the discretized l2 loss instead of the negative log-likelihood (ablation) | FaDIn · Univariate simulated Hawkes, RC/TG/TE kernels | parameter estimation accuracy | No clear effect |
| Use a general parametric (raised cosine) finite-support kernel with FaDIn instead of non-parametric histogram kernels | FaDIn · Simulated 2-dim Hawkes with raised cosine kernels, T in {10^3,10^4,10^5} | normalized l1 error on intensity and computation time | Helped |
| Increase kernel support length W for Truncated Exponential kernel in FaDIn (ablation) | FaDIn · Synthetic 1-dim Hawkes with Truncated Exponential kernel | l2 error of parameters and computation time | Mixed |
| Use a raised cosine kernel (no predetermined support) instead of truncated Gaussian for MEG atom latency | FaDIn on MEG data · MNE sample and somato MEG datasets | sharpness of intensity peaks / latency estimates | Helped |
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